Grant: $303,125 - National Science Foundation - Jul. 10, 2009
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Award Description: Intellectual merit: The PI proposes to study the structure, its robustness/stability and transitions of the large scale atmospheric and oceanic flows, to yield a better understanding of the atmospheric and oceanic prediction and predictability relevant to typical sources of their low frequency variability. The proposed work focuses on three sources of atmospheric and oceanic variability: the wind driven ocean circulation, the thermohaline circulation and the El Ni˜no Southern Oscillations (ENSO). Their variability, independently and interactively, may play a significant role in climate changes, past and future. The wind-driven circulation plays a role mostly in the oceans’ subannual-to-interannual variability, while the thermohaline circulation is most important in decadal-to-millenial variability. ENSO is the known strongest interannual climate variability associated with strong atmosphere-ocean coupling, which has significant impacts on global climate. The study involves, on the one hand, applications of the existing mathematical theory to the understanding of the underlying problems, and, on the other hand, the development of new mathematical theories. Three new theories—dynamic transition theory, geometric theory for incompressible flows, and the attractor bifurcation theory– are developed recently by Ma and the PI, under close links to the physics. In return the theories are applied to the physical problems. In fact, with these new theories, many longstanding problems in nonlinear science and engineering are either solved or becoming more accessible, leading to better understanding and to a number of new physical predictions for the problems. Part of the proposed study is on further development of the dynamic transition theory. The main philosophy of the theory is to search for the full set of transition states, giving a complete characterization on stability and transition. The set of transition states —-physical reality —- is represented by a local attractor. Following this philosophy, the dynamic transition theory is developed to identify the transition states and to classify them both dynamically and physically. The PI uses a combination of physical modeling, asymptotic methods, rigorous mathematical theory, and large scale computing to yield new insights into physical phenomena. The proposed research involves specific collaborations with active atmosphere/ocean scientists in different institutions including Michael Chekroun (UCLA), Henk Dijkstra (Utrecht U., Netherlands), M. Ghil (ENS Paris & UCLA), and R. Samelson (Oregon State). It is hoped that the proposed studies could lead to improved predictions and new insights of weather, climate, and environmental phenomena of central importance to our economy. Broader impact: An important secondary goal of the project is to advance discovery and understanding while promoting teaching and learning. The PI continues his effort on broader impacts of the proposed project. First, the PI is supervising three advanced and two second year Ph D students working on the proposed project. Meanwhile, the PI intends to teach two topic courses for graduate students in the grant period. Second, the PI intends to write two books during the grant period: one pedagogical first year graduate textbook on ordinary differential equations focusing on dynamic transitions, based on the teaching materials and on the proposed research, and a research monograph on Phase Transition Dynamics in Nonlinear Sciences. Both books will be important part of the proposed research activities. Finally, the PI will continue to organize meetings and workshops.
Project Description: The PI studies factors that are relevant to the low-frequency variability of atmospheric and oceanic flows and that play a role in climate changes. He focuses on three sources of atmospheric and oceanic variability: the wind-driven ocean circulation, the thermohaline circulation, and the El Nino Southern Oscillations (ENSO). The study involves applications of existing mathematical theory to the understanding of the underlying problems and the development of new mathematical theories -- dynamic transition theory, geometric theory for incompressible flows, and attractor bifurcation theory -- that are applied to the physical problems. These new theories also have application to other problems in nonlinear science and engineering. The main idea of dynamic transition theory is to search for the full set of transition states, giving a complete characterization of stability and transition. The set of transition states -- physical 'reality' -- is represented by a local attractor. Following this line, dynamic transition theory is developed to identify the transition states and to classify them both dynamically and physically. The project involves specific collaborations with atmosphere/ocean scientists in different institutions and includes training of graduate students. The investigator studies some typical sources of climate variability, which, independently and interactively, play a significant role in climate changes. Wind-driven circulation plays a role mostly in the oceans' subannual-to-interannual variability, the El Nino Southern Oscillations are associated with interannual variability, and the thermohaline circulation is most important in decadal-to-millenial variability. The investigator undertakes a careful fundamental-level examination of these phenomena. Graduate students are involved in the project. The studies could lead to improved predictions of and new insights into weather, climate, and environmental phenomena of central importance to our economy.
Jobs Summary: Additional Pay: Acad Services (Total jobs reported: 0)
Project Status: Less Than 50% Completed
This award's data was last updated on Jul. 10, 2009. Help expand these official descriptions using the wiki below.